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An 8mm solid state spectometer Lee, Ker Ping 1962

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AN 8mm SOLID STATE SPECTROMETER by KER PING LEE B.Sc, Chung Chi College, 1960  A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE i n the Department of PHYSICS  We accept this thesis as conforming to the required standard  THE UNIVERSITY OF BRITISH COLUMBIA December, 1962  In presenting this thesis i n p a r t i a l fulfilment of the requirements for an advanced degree at the University of B r i t i s h Columbia, I agree that the Library s h a l l make i t freely available for reference and study.  I further agree that permission  for extensive copying of this thesis for scholarly purposes may  be  granted by the Head of my Department or by his representatives. It i s understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission.  Department of The University of B r i t i s h Columbia, Vancouver 8, Canada. Date  -ii-  ABSTRACT  A s e n s i t i v e , wide or narrow band, s o l i d state  spectrometer  operating at a wavelength of 0.85 cm has been b u i l t which i s described i n d e t a i l .  The spectrometer i s of the c r y s t a l  reflection-cavity-in-magic-Tee-bridge  type and can operate from  room down to l i q u i d helium temperatures. the  TE-JJJL  detector  The cavity Is excited In  mode and the magnetic f i e l d modulated at 140 cps.  Both  large and small f i e l d modulations are incorporated for scope presentation of linewidth varying from about 0.5 to 500 gauss. Signals from single crystals of copper sulphate pentahydrate and p o l y c r y s t a l l i n e l - l - d i p h e n y l - 2 - p i c r y l hydrazyl (DPPH) have been obtained.  From the l a t t e r ,  a sensitivity  l i m i t of about 10  gram  i s obtained at room temperature for a bandwidth of 1 cps Indicating a sensitivity  of the order of 1 0 ~ ^ gram at 4 . 2 ° K.  Various methods  of improvement were discussed i n order to reach the ultimate sensitivity.  -iii-  ACKNOWLEDGMENT  The research described i n t h i s thesis was supported.by the National Research Council of Canada through the research grant to Dr. J . V e i t and the award of two summer assistantships (1961,62) to the author. I am indebted to Dr. J . V e i t who f i r s t introduced me to the present f i e l d .  To Dr. I F i r t h , I am grateful for h i s valuable  assistance without which the thesis could not have been completed. I wish to akcnowledge the generosity  of Dr. G. Voss of the  E l e c t r i c a l Engineering Department for lending me the EMI klystron o s c i l l a t o r used i n the  experiment.  I am much thankful to Mr. J . Banner whose incessant aid throughout the construction of the apparatus as well as the experiment has been greatly appreciated. The members of the Physics Work Shop have been very I would l i k e to thank, e s p e c i a l l y ,  cooperative.  Mr. A. Fraser for making a l l the  microwave c a v i t i e s used i n the experiment and Mr. J . Lees for building the vacuum system. I wish also to thank Mr. J . Felton and Mr. R. Weissbach for supplying the l i q u i d nitrogen and l i q u i d helium and Mr. D. Y. Chung for  a s s i s t i n g i n t r a n s f e r r i n g l i q u i d helium. F i n a l l y , acknowledgment i s made to Dr. R. Howard and Dr. J . B.  Brown for t h e i r kindness i n reading the manuscript.  -iv-  TABLE OF CONTENTS Page ABSTRACT  ..  ii  ACKNOWLEDGMENT  iii  LIST OF TABLES  vi  LIST OF ILLUSTRATIONS  vi. •  LIST OF PLATES  vii  CHAPTER I II  INTRODUCTION . . ,  1  QUANTUM THEORY OF PARAMAGNETISM  3  2.1 The Magnetic Resonance Phenomenon 2.1.1 Resonance Condition 2.1.2 Fine Structure 2.1.3 Hyperfine Structure 2.2 Theory of Line Width 2.2.1 Spin-Lattice Interaction 2.2.2 Spin-Spin Interaction 2.2.3 Exchange Interaction 2.3 Effect of C r y s t a l l i n e F i e l d 2.4 The Theoretical Hamiltonian III  IV  i  3 3 4 5 6 6 7 8 9 .10  DESCRIPTION OF APPARATUS  15  3.1 Introduction 3.2 The Microwave System 3.2.1 The Microwave Power Source 3.2.2 Waveguide Components 3.2.3 C r y s t a l Detectors 3.2.4 The Cavity Resonator 3.2.5 Wavelength Measurement 3.3 Magnetic F i e l d Equipment 3.3.1 The Magnet 3.3.2 The Magnet Power Supply 3.3.3 Low Frequency Modulation 3.4 The Detection System 3.5 The Vacuum System  15 15 .15 .16 16 17 17 17 17 18 19 19 20  EXPERIMENTAL PROCEDURE  22  - V -  CHAPTER V  Page EXPERIMENTAL RESULTS  26  5.1 Introduction ... 5.2 General Information . . . . . . , 5.3 Results  26 27 28  CONCLUSION AND DISCUSSION  32  :  VI  Appendix  34  Bibliography  40  -vi-  LIST OF TABLES TABLE  Page  1  S e n s i t i v i t y of Q-band Spectrometer Obtained  .  30  2  Comparison of S e n s i t i v i t y of Different  Spectrometers . . .  31  LIST OF ILLUSTRATIONS To Follow Page  FIGURE 1  Energy Level Diagram for S = 3/2 ion with Magnetic F i e l d H p a r a l l e l to the Axis of C r y s t a l l i n e F i e l d  4  2  Electronic S p l i t t i n g s of C u  4  3  Block Diagram for 8 mm Microwave C i r c u i t  15  4  Cross-Section  17  5  Block Diagram of a Single Modulation Spectrometer  25  6  A Schematic Diagram of the Vacuum System .,  20  7  The Cryostat  20  8  Signals from 2 mg of CuS0 '5H 0 Single C r y s t a l  .28  9  Signal from 0.2 mg of Powder DPPH  28  2 +  of" the Cavity  :  4  2  -vii-  LIST OF PLATES To Follow PLATE I II III  Page View of the Main Microwave Arrangement . . . . . . . . .  15  View of the Magnet and the Cryostat  .15  General View of the Apparatus  ......  42  -I-  CHAPTER I  INTRODUCTION  Magnetic resonance i s a branch of radio-frequency spectroscopy invaluable to the study of the s o l i d state.  It can be c l a s s i f i e d into  nuclear, ferromagnetic, antiferromagnetic and paramagnetic resonance. Nuclear resonance i s concerned with nuclear dipoles, the others with electronic dipoles.  In ferromagnetic and antiferromagnetic  substances,  the electronic dipoles are strongly coupled together by exchange  forces  while i n paramagnetic materials, the electronic dipoles form a loosely coupled system; each paramagnetic ion may be treated i n d i v i d u a l l y . The phenomenon of paramagnetism occurs whenever a system of charges has a resultant angular momentum.  I f t h i s momentum i s of  electronic o r i g i n , one speaks of electronic paramagnetism.  For  instance, paramagnetism can be found i n atoms and molecules having an odd number of electrons, i n molecules with an even number of  electrons  but having a resultant angular momentum, i n the so-called colour centres, i n metals and semiconductors (caused by conduction electrons). The properties of-the paramagnetic ion can be obtained from measurements of the s u s c e p t i b i l i t y , s p e c i f i c heat, gyromagnetic r a t i o , Faraday e f f e c t , paramagnetic relaxation and paramagnetic resonance.  However  only the l a s t method enables studies to be made from the microscopic  -2-  point of view.  It i s also more sensitive than any of the other methods.  Consequently, i t can deal with very small quantities of paramagnetic substance.  This i s very convenient and often  advantageous.  A considerable amount of research has been carried out on microwave absorption i n s o l i d state compounds and most attention has been given to paramagnetic resonance absorption.  The results obtained from an analysis  of these spectra give considerable information on forces and interactions existing i n the s o l i d state.  Paramagnetic resonance gives the most  direct and accurate description of the ground state and of the effect of c r y s t a l l i n e f i e l d on the energy l e v e l s of the paramagnetic i o n .  Its  high s e n s i t i v i t y also permits the perturbations of the nuclear spin and nuclear e l e c t r i c quadrupole moment to be detected. In t h i s t h e s i s , we s h a l l be concerned with the design of a spectrometer suitable for such studies.  A short account of the theory  of paramagnetic resonance w i l l be given i n Chapter I I .  Chapters III and  IV give the descriptions of the apparatus and the experimental procedure in detail.  Following are the experimental results obtained from the  testing of the  spectrometer.  -3-  CHAPTER II  QUANTUM THEORY OF PARAMAGNETISM  Excellent summaries of the experimental and t h e o r e t i c a l aspects of paramagnetic resonance can be found i n the review a r t i c l e by Bleaney and Stevens (B4) and i n a complementary review by Bowers and Owen ( B 5 ) . In this chapter, the theory w i l l be b r i e f l y discussed.  For more d e t a i l ,  the reader i s referred>to the above-mentioned a r t i c l e s together with the texts by Low (L2) and Ingram ( I I ) .  2.1 2.1.1  The Magnetic Resonance Phenomenon Resonance Condition If  a free ion of a resultant angular momentum J i s placed i n a  uniform magnetic f i e l d H, the energy l e v e l s corresponding to the various s p a t i a l orientation of J. are given by  W = g ^HM  , g i s the Lande g factor and  eh i3 = ^-^  (2.1)  I  s  "the Bohr magneton; e, m  are the charge and mass of the electron, c i s the v e l o c i t y of l i g h t , h i s Planck's constant, M i s the component of J along the f i e l d acting on the i o n .  I f an alternating f i e l d " o f frequency V  i  s  applied at r i g h t  -4-  angles to H, magnetic dipole t r a n s i t i o n s are produced when  h V  according to the selection rule  = g£H  (2.2)  A M = 1 1.  In a system of ions i n thermal equilibrium with t h e i r surroundings, the lowest state has the greatest population.  Since t r a n s i t i o n s up and  down have the same a p r i o r i p r o b a b i l i t y , the net r e s u l t i s a greater . absorption than emission of energy causing a damping of the tuned c i r c u i t with which the paramagnetic substance i s coupled.  2.1.2  Fine Structure The degeneracy of the ground state of a paramagnetic ion i n a c r y s t a l i s often l i f t e d by the c r y s t a l l i n e e l e c t r i c f i e l d and other interactions.  Consider an ion of spin 3/2 with an i n i t i a l s p l i t t i n g  between the doublets M field:(Fig. l ) .  = 1 \ and M  = - 3/2 due to an a x i a l c r y s t a l l i n e  The energy l e v e l s diverge l i n e a r l y when a magnetic  f i e l d i s applied along the axis which i s taken as the axis of quantization.  An o s c i l l a t i n g magnetic f i e l d component perpendicular to the £  axis induces t r a n s i t i o n s transitions  iM  g  =0.  A M = ± 1 and the p a r a l l e l component induces s  In  A M = - 1 t r a n s i t i o n s , a t r i p l e t structure s  results when the frequency i s kept constant as indicated by the arrows i n F i g . 1 and the magnetic f i e l d i s varied.  This forms the  'fine  structure' of the spectrum. 2+ • In Cu  ion shown i n F i g . 2 (11), most of the t o t a l  degeneracy•of  (2L+1)(2S+I) = 10 i s removed by the cubic and tetragonal f i e l d s of the  To f o l l o w page 4 M  s  Initial splitting by crystalline • field  H  increasing  F i g . 1 Energy L e v e l Diagram for S=3/2 ion with Magnetic F i e l d H Parallel to the A x i s of the Crystalline F i e l d .  /  2  Ground State  m  t  /  D  , \\  f  i i i i i  » ~  \ « » » »  • /  /  /  /  %  \  »  El  \  Free  Cubic  Ion  Field  Fig.2  Tetragonal Field  Electron Splittings of C u  Spin-orbit Coupling  +2  £ h » = g^H Magnetic Field  -5-  crystalline lattice,  the whole of the degeneracy being removed by the  addition of the s p i n - o r b i t i n t e r a c t i o n .  According to Kramers theorem.(K2)  an ion having an odd number of electrons must have i t s energy l e v e l s remain two-fold degenerate and the degeneracy can be raised only by an applied magnetic f i e l d .  Since the o r b i t a l s p l i t t i n g s are very large a l l  the copper ions w i l l be i n the lowest state Ej_, and we have a paramagn e t i c resonance absorption spectrum without fine structure.  2.1.3.  Hyperfine Structure When the nucleus of a paramagnetic ion also possesses a resultant  angular momentum I and hence a magnetic moment, there w i l l be an i n t e r action with the electronic motion..  In-a strong external magnetic f i e l d ,  each electronic l e v e l i s s p l i t into (21+1) l e v e l s due to the (21+1) different orientations of the nucleus.  The o s c i l l a t i n g f i e l d exerts  a n e g l i g i b l e effect on the nuclear moment (about 10 that of the electron) • This together with lines.  times smaller than  so that the allowed t r a n s i t i o n s become  A. Mj = 0.  A M = i l selection rule gives (21+1) hyperfine g  Since at normal temperatures a l l nuclear orientations are  equally probable, the l i n e s w i l l have equal i n t e n s i t y .  Also i n a strong  f i e l d , the energy l e v e l s vary l i n e a r l y with the f i e l d .  The l i n e s are  therefore equally spaced.  I f the external f i e l d i s comparable to that  produced by the nucleus, the component hyperfine l e v e l s w i l l contain an admixture of different Mj states giving r i s e to unequal s p l i t t i n g of the l e v e l s .  When two states contain the same value of M j , a t r a n s i t i o n  i s allowed which appears to be "forbidden" when the states are l a b e l l e d by t h e i r strong f i e l d quantum numbers.  -6-  Another cause of unequal spacing i s due to the interaction of the nuclear e l e c t r i c quadrupole moment with the gradient of the f i e l d produced at the nucleus.  electric  I f the applied f i e l d i s p a r a l l e l to the  gradient of the e l e c t r i c f i e l d , t h i s interaction w i l l s h i f t the energy 2 l e v e l s by an amount proportional to Mj .  I f the two directions are not  p a r a l l e l , the various nuclear states are admixed and forbidden t r a n s i tions r e s u l t as before. 2.2  Theory of Line Width Very often, the resolution of the fine structure and hyperfine structure i s l i m i t e d , not by instrumental e f f e c t s , but by the l i n e widths of the absorption l i n e s .  This width i s dependent upon the intei?-  action between the paramagnetic ions and t h e i r surroundings and on the interaction among the ions themselves.  The natural l i n e width arises  from the f i n i t e l i f e t i m e of a given state and i s completely compared with the other factors  (ll).  negligible  It w i l l not be discussed here.  The other more important sources of broadening w i l l be b r i e f l y treated below..  2.2.1  Spin-Lattice Interaction The s p i n - l a t t i c e  interaction may be characterized by a s p i n - l a t t i c e  relaxation time T-^ which i s a measure of the rate at which a spin system approaches equilibrium with the l a t t i c e the absorption of energy.  after having been disturbed by  The mechanisms have been discussed by many  authors (L2). There i s the i n d i r e c t process or Raman process i n which the  spins  -7-  transfer energy with the l a t t i c e by means of i n e l a s t i c  scattering of  2 7 phonons.  For the case of S = 1/2, Tj_ cC  temperature @ ^ and proportional to  ^6/ \  for  T  T> ®  for T < n  .  A  Debye  i s the  height of the next o r b i t a l above the ground state and A. i s the s p i n - o r b i t coupling  coefficient.  I f the spins exchange a quantum of energy d i r e c t l y with a l a t t i c e vibration of the appropriate frequency, we have the d i r e c t process. —2 — 1 Then T^  0  0  H T  and Tj_ °c H ^T"~^ -  for non-Kramers s a l t s (even number of electrons) f o r Kramers s a l t s .  The Orbach process (01), a r i s i n g  from phonon resonance e f f e c t s , gives T-j_ oC. exp (  ^/kT).  S p i n - l a t t i c e relaxation i s the predominant l i n e broadening mechanism at high temperatures.  In practice the temperature at which  measurements are made i s always reduced u n t i l the l i n e width Is due to spin-spin rather than s p i n - l a t t i c e 2.2.2  interaction.  Spin-Spin Interaction The second broadening effect arises from the i n t e r a c t i o n between the dipoles which can be regarded as rather l i k e bar magnets precessing about the external f i e l d .  The component i n the f i e l d direction sets up  a steady f i e l d at the neighbours a l t e r i n g the t o t a l f i e l d value  slightly.  This process of broadening i s s i m i l a r to that produced by an inhomogeneous magnetic f i e l d .  Also the rotating component sets up a rotating  f i e l d which may induce t r a n s i t i o n s decreasing the normal l i f e t i m e  i n the neighbouring ions and thus  of the energy state.  A broadening  r e s u l t s as a consequence of the Uncertainty P r i n c i p l e . The theory of spin-spin interaction has been developed by  Van Vleck (V2) and Pryce and Stevens (P4).  For free spins, the mean-  square width as given by Van Vleck i s  \ = i sCS+ne A 51 2  2  2  2  l-Scos^Q  >  2  I  2  3*  (2.3)  where 0 i s the angle between the l i n e s joining the dipoles and the d i r e c t i o n of the applied f i e l d r being the distance between the j and kth i o n . The second term refers to i n t e r a c t i o n between d i s s i m i l a r ions. This dipolar i n t e r a c t i o n can also be described by a relaxation time T 2 as defined by  T  2 = \ TgCV)]  ^ L.  (2.4)  Jmax  where g ( V ) i s the normalised l i n e shape function.  2.2.3  Exchange Interaction If  the paramagnetic ions are close enough together exchange i n t e r -  action may occur between them, which can a l t e r the l i n e width considerably.  When the spins are i d e n t i c a l and S = 1/2,  Van Vleck (V2) shows  that the exchange i n t e r a c t i o n contributes to the fourth moment but not to the second moment of an absorption l i n e .  Since the t o t a l area of  -9-  the l i n e cannot change, the l i n e w i l l be. peaked and the extra area d i s tributed i n the wings.  This i s exchange narrowing.  For d i s s i m i l a r ions, such as ions precessing about different axes., the exchange i n t e r a c t i o n tends to bring the two different together and hence produce one wider l i n e .  transitions  In other words, the exchange  i n t e r a c t i o n contributes to the second moment and we have exchange broadening.  In general, both exchange broadening and exchange narrowing are  present and the resultant l i n e width depends on the r e l a t i v e contribution of each. The effect of exchange i n t e r a c t i o n i s well exemplified i n the test samples.  Copper sulphate shows exchange broadening as a r e s u l t of the  coalescence of the two l i n e s due to the two d i s s i m i l a r Cu unit c e l l (Bl).  ions i n the  For DPPH free r a d i c a l s , considerable exchange narrowing  r e s u l t s ' i n a very narrow l i n e width even i n a p o l y c r y s t a l l i n e sample (H2).  2.3  Effect of C r y s t a l l i n e F i e l d As indicated i n section 2.1.2, a paramagnetic ion i n a c r y s t a l i s subjected to a strong inhomogeneous e l e c t r i c f i e l d c a l l e d the c r y s t a l l i n e electric field.  This f i e l d originates i n the environment of the p a r a -  magnetic ion and consists of (a) s t a t i c and (b) fluctuating components. The latter, i s due to the thermal v i b r a t i o n of the l a t t i c e and c o n t r i butes only to the l i n e width (see  section 2.2.1).  The s t a t i c  component,  to the f i r s t approximation, w i l l have the same symmetry as the c r y s t a l structure.  Its effect i s to cause a Stark s p l i t t i n g of the energy  l e v e l s of the Ions thereby removing some of the (2J+1) degeneracy;  -10-  (J=L+S).  The degree to which t h i s degeneracy i s l i f t e d depends on the  symmetry of the f i e l d . Experimental data reveals that the strength of the various c r y s t a l l i n e f i e l d s f a l l into three groups. (i)  In the weak f i e l d case, L and S are not uncoupled but s t i l l  precess around the resultant J which- i n turn precesses about the d i r e c t i o n of the applied e l e c t r i c f i e l d .  Good examples are the rare earth  s a l t s where the unpaired 4f electrons are somewhat shielded from the d i r e c t influence of the c r y s t a l l i n e ( i i ) Medium F i e l d s .  field.  The coupling between L and S Is broken so  that they precess about the f i e l d separately and J i s no longer a good quantum number. quenched. (iii)  It i s found that the o r b i t a l motions are usually  For example the iron group hydrated s a l t s . The f i e l d may be so strong as to destroy both the LS coupling  and the coupling between the angular momenta and spins of the i n d i v i d u a l electrons.  Again the o r b i t a l motion i s quenched.  This i s t y p i f i e d by  the iron group cyanides.  2.4  The Theoretical Hamiltonian The Hamiltonian of an ion i n a c r y s t a l l a t t i c e the sum of a ..number of interaction terms.  can be written as  The exact solution i s usually  obtained for the largest term and the contributions of the remaining terms taken into account by perturbation c a l c u l a t i o n s .  The various  terms' are: (a) The Coulomb interaction of the electrons with the nuclear charge Ze and the mutual repulsion of the electrons.  In the  -11-  n o n - r e l a t i v i s t i c approximation, i t i s given by.  N  N  W  F  21  =  ( P  k  /  2  m  ~  Z  e  / k) r  +  r  6 /r  kj  k > j=l  k=l where P  Yl  k  = l i n e a r momentum  k  = radius vector from nucleus t o electron.  (b) The magnetic i n t e r a c t i o n between the e l e c t r o n spin s^. with the o r b i t a l momentum l .  .  k  WLS 3k  where  a  j k ' ^jk» j k c  constants.  a r e  (c) The mutual i n t e r a c t i o n between the e l e c t r o n i c spins  *j • k  3(r- • S - P O ^ •  s  V  Woo -  ^  k  L  3  k  r  3k  3k  (d) The i n t e r a c t i o n energy due t o the nuclear s p i n I and nuclear quadrupole moment Q.  2  %  3 - —  4- i  eQ 2  w  Q  21(21 -  1)  Ik I  +  1(1  ~  + 1)  5"  ~  +  — ^ O k H  3 ( r . I)k  Here ^> ^ and "Y r e f e r t o the nuclear magneton and nuclear  '  1  -12-  gyromagnetic r a t i o . ..(e) The effect of the external magnetic f i e l d H which produces the s p l i t t i n g of the electronic l e v e l s between which the t r a n s i t i o n s are observed.  (f)  The d i r e c t i n t e r a c t i o n of the nucleus with the external f i e l d .  \  •-t e  •  H N  1  (g) The i n t e r a c t i o n of the c r y s t a l l i n e e l e c t r i c f i e l d .  W =  eV(x  y  where  k5  V^x^, y^., z-^) i s the p o t e n t i a l .  y ,  z )  k  k  The general Hamiltonian i s  therefore given by  ^  = W + W + W F  y  LS  + W  s s  + W + W 4- W + W H  N  Q  The order of magnitude of these interactions are Wp ^ Wy 'n-  10  W ~»  10  N  3  - 1  10  -  4  10~  -1  cm 3  , W-^g ^ 1 0  cm , - 1  2  W Q ^ - 10~  - 1 '  3  cm  , Wgg ^  -  10  3  c m , and W^. ~ - 1  (2.5)  h  10^ cm ^~, -1 cm , W^ ^  10~  3  -1  cm  ,  cm" . 1  I f we confine our discussion only to states which are eigenstates of L and S, eon. ( 2 . 5 ) can be written as a sum involving terms representing electronic interactions and terms representing nuclear i n t e r a c t i o n s .  -13-  A perturbation method of c a l c u l a t i o n has been given by Pryce (P3) i n which the operators r e f e r r i n g to spin and nuclear variables are treated as non-commuting algebraic quantities. components of S and I i s obtained.  An expression involving the  This i s c a l l e d the 'Spin Hamiltonian'  whose f i r s t order approximation gives  3f=  S-.-D'S+pH'g-.S + S ' T ' I + I ' P ' I  - p  2  H • A  s  z  + B(S I  N  H • I -  z  g p N  X  X  + S I ) y  y  N  H • I  • H  (2.6)  I f the c r y s t a l l i n e f i e l d has a x i a l symmetry about the  + AS I  - T^  + p [ l /  2 z  z-axis,  - \ S(S + 1)  - |  1(1 + l ) j  £ H' A ' H  (2.7)  S here i s the effective electronic spin and i s determined by equating the m u l t i p l i c i t y of the l i n e observed to 2S.  The term i n D describes how  the l e v e l s behave i n zero magnetic f i e l d i n the absence of nuclear interaction.  -g  f  and g  x  are the g values when the f i e l d i s applied  p a r a l l e l and perpendicular to the c r y s t a l l i n e e l e c t r i c f i e l d axis respectively.  A and B measure the s p l i t t i n g of the hyperfine structure.  P refers t © the quadrupole s p l i t t i n g and i s related to Q through p = 3eQ ^ 3 ^ X ^ / 4 1 ( 2 1 - 1).  The f i n a l term - a? H • i\ • *H  representing  -14-  a constant i n t e r a c t i o n independent of S or I i s normally very small and can be neglected.  The actual energies are then given by the  eigenvalues of the new operator where  i n the equation  l^'ty-  represents the wave functions of the effective  E l|^ 0  spin states.  -15-  CHAPTER III  DESCRIPTIONS; OF APPARATUS  3.1  Introduction The essential  elements of a microwave s o l i d state  spectrometer  are (a) a monochromatic source, preferably of variable frequency, (b) a cavity (absorption or r e f l e c t i o n  type),  (c) a variable magnetic f i e l d , and (d) a detector. In t h i s chapter, the components of the narrow band, single modulat i o n spectrometer are described i n d e t a i l .  Block diagrams w i l l be  employed to i l l u s t r a t e the design p r i n c i p l e s and the actual c i r c u i t diagrams are collected together i n the appendix.  The spectrometer can  function from room to helium temperatures.  3.2  The Microwave System The Block diagram for the microwave setup Is shown i n F i g . 3.  The  photograph i n Plate I shows the general arrangement of the microwave components. 3.2.1  The Microwave Power Source Besides having a variable frequency source, a good spectrometer further requires that  To follow page 15  MATCHEP LOAD  STUB TUNER  KLYSTRON  rlSOLATOl ?  ATTN  DIREC C Q  Upi.F.R  H  MAGIC  TEE  FXR SUPPLY  .  ATTN 1  WAVEMETER  ATTN < •  STUB TUNER  1 IN53 XTAL  F i g . 3 Block Diagram for 8mm Microwave C i r c u i t .  IN53 XTAL  CAVITY  T o follow page i5  PLATE II  VIEW OF THE MAGNET AND THE CRYOSTAT  -16-  (a) the frequency and power be s u f f i c i e n t l y  stable,  (b) there must be enough power output (usually of the order of milliwatts),and (c) a low noise l e v e l i s desirable for good resolution and sensitivity. In the present experiment an EMI valve type reflex klystron (VX5023T) capable of generating about 50 mW of power i s used.  This klystron i s  tunable from 34.6 to 36.4 Gc/s and i s forced a i r - c o o l e d . In order to satisfy r i p p l e power supply.  (a), i t i s necessary to have a stable low  We have chosen an FXR Model Z815B Universal  Klystron Power Supply Unit with a regulation of better than 0.3%.  The  rms r i p p l e voltage i s less than 3 mV for the beam voltage and l e s s than 1 mV on the r e f l e c t o r .  Saw-tooth, square-wave,sine wave and pulse  modulations are available at various voltage l e v e l s and frequencies. In the experiment, only saw-tooth modulation was used to sweep through the k l y s t r o n r e f l e c t o r mode. 3.2.2  Wave-Guide Components A l l of the wave-guide components are commercial units manufactured by the DeMornay Bonardi Corporation except for the c i r c u l a t o r which i s a Cascade Research product.  This unit i s used to i s o l a t e the microwave  source from the rest of the system (G2). 3.2.3  Crystal Detectors For the detection and monitoring of the microwave power 1N53 s i l i c o n diodes are used.  These are designed for a centre frequency of  35.0 Gc/s and are mounted on broad-band c r y s t a l mounts.  -17-  3.2.4  The Cavity Resonator A c i r c u l a r c y l i n d r i c a l cavity resonator operating i n the H-^-^ mode has been designed from data given by Wilson (W2).  It i s made -of brass.  The choice of the fundamental mode of excitation has the advantage of concentrating the microwave energy at the bottom of the cavity where the sample can be conveniently placed.  Care has been taken to choose  a size as large as possible within the l i m i t a t i o n of the magnet gap such, that no interference modes nor crossing modes can e x i s t .  This  l a t t e r precaution reduces the trouble of determining the mode of e x c i t a t i o n i n the cavity which i s very troublesome at 8 mm and below. cavity used i s a fixed size one.  The  However, i t i s r e l a t i v e l y simple to  convert to a'tunable cavity by incorporating a choke plunger as the termination.  The Q of the cavity i s of the order of 2000 at room  temperature and the diameter and thickness of the coupling hole are respectively 1.5 and 0.2 mm. 3.2.5  Wavelength Measurement A broadband absorption type low Q cavity frequency meter i s employed as an estimate of the klystron frequency by monitoring the power from a - d i r e c t i o n a l coupler ( F i g . 3).  It i s a Sperry product and  i s suitable for operation i n the range of 26.5 - 39.0 Gc/s. lute accuracy i s about 0.1%.  The abso-  This low Q wavemeter i s convenient for  a rapid estimate of the frequency of the k l y s t r o n .  For more precise  work, a high Q wavemeter should be included.  3.3 3.3.1  Magnetic F i e l d Equipment The Magnet A magnetic f i e l d i n t e n s i t y of over 10 kilogauss i s produced by  To follow page 17  Rectangular German Silver Guide Supporting Brass Block Tuning Screws Solder Flux Screw(No. 000-120) Coupling Flange  ]  ~ A l Coupling D i s c  7.6 Brass Cavity  Sample 9.2  Fig. 4  C r o s s - s e c t i o n of the C a v i t y .  ( A l l Dimensions in m m . )  -18-  a small electromagnet  designed by Buckmaster and p a r t l y constructed i n  the departmental machine shop.  For f u l l e r d e t a i l s ,  be made to H. A. Buckmaster s thesis (B6). 1  reference should  B r i e f l y , the main features  are (a) adjustable gap up to 3" (b) rotatable magnet yoke ( 3 6 0 ° with 0 . 5 ° c a l i b r a t i o n ) (c) v e r t i c a l l e v e l  adjustment  (d) water cooled (e)  good homogeneity of the order of 0.5%  (f)  t r o l l e y mounting for ease of moving.  Plate II shows the view of the magnet with the cryostat. 3.3.2  The Magnet Power Supply The magnet current of up to 15 amperes i s supplied by 51 twin-triode tubes (6AS7G) connected i n p a r a l l e l .  The grids are biased to near  c u t - o f f with a regulated power supply (see Appendix). voltage used i s 220 v o l t s .  The normal plate  This i s obtained by connecting two generators  i n series since each generator i n the Physics Building can give only 150 v o l t s maximum. The s t a b i l i t y thus produced has been measured to be of the order of  <  0.5%.  This was done by comparing the voltage developed across  a standard manganin r e s i s t o r  (0.124 ohm) with a standard mercury c e l l  and the difference detected by a Honeywell n u l l i n d i c a t o r .  The f i e l d  s t a b i l i t y should be much higher since the magnet i s working near saturation.  Signal from DPPH have been recorded i n d i c a t i n g that the 4  s t a b i l i t y approximates to 1 i n 10 . for most applications.  Such s t a b i l i t y i s  sufficient  However, i t must be emphasized that higher  s t a b i l i t y i s required for narrower l i n e s than that of DPPH ( ~ 4 gauss).  With the use of t r a n s i s t o r s , i t becomes r e l a t i v e l y  -19-  inexpensive to b u i l d a supply having s t a b i l i t y of the order of 1 i n 10 or better ( G l ) . 3.3.3  Low Frequency-Modulation A sinusoidal current source i s used to drive a p a i r of Helmholtz c o i l s for low frequency f i e l d modulation.  The modulator consists of  a 6AU6A driver tube whose grid input i s fed from an a u d i o - o s c i l l a t o r (Beckman/Shasta Model 301A) and the output i s used to control the current flowing through 14 6AS7-tubes a l l connected i n p a r a l l e l (Appendix).  By  t h i s means, a large modulation can be obtained. For the study of narrow l i n e s such as DPPH signals some d i f f i c u l t y arises i n the production of small modulation because of the great number of turns of wire (350 turns) i n the Helmholtz c o i l s .  A convenient  solution i s to shunt the c o i l s with a variable load.  In our case, a  3.2 ohm rheostat i s used which can be disconnected whenever a large modulation i s needed.  3.4  The Detection  System  "A three stage, low noise, variable gain amplifier (2.10^ maximum) of standard design i s used to amplify signals from the c r y s t a l detector. The design data has been taken from an RCA Receiving Tube Manual (Tech. Series RC-19, 1959). filaments  A t y p i c a l noise l e v e l i s about 2y V input.  The  are d.c. heated to reduce hum and the plate voltage i s  obtained from a regulated Lambda-power supply.  It i s found that 60 c/s  pickup exists despite the precautions taken including the use of coaxial '• cables between stages. Following the high gain amplifier i s a f i l t e r - a m p l i f i e r to reduce  -20-  noise.  This i s a low gain device and employs a t w i n - f i l t e r with a  bandwidth of 20 c/s and centre frequency 135 c/s  (Vl).  In t h i s way i t  i s possible to eliminate 60 cps pickup completely. ' Before passing on to a pen-recorder for a permanent record, the amplified signal i s fed into a phase sensitive detector. follows very closely the one due to Schuster ( S i ) .  The design  Normally a band-  width of 1 or 2 c/s i s employed and the recorded signal i s the d i f f e r e n t i a l of the absorption l i n e . Detailed c i r c u i t s of a l l the electronic Instruments can be found i n the Appendix.  3.5  The Vacuum System Experimental techniques at low temperatures are well known (Wl). In t h i s section, only a b r i e f description w i l l be given. A schematic representation of the vacuum i n s t a l l a t i o n i s shown i n , F i g . 6.  and M2 are the mercury and o i l manometers for measuring  pressure i n the dewar.  The Cenco Supervac o i l diffusion pump used i s  for high speed evacuation down to about a micron of mercury pressure. This i s preceded by a backing pump (Cenco Pressovac) capable of producing about 10 microns of pressure.  The backing pump, besides pumping down one  arm of the manometer, i s also used to evacuate the jackets of the transfer syphon and that of the helium dewar. Fig.  7 depicts a double dewar cryostat arranged concentrically so  that the outer forms a l i q u i d nitrogen space, surrounding the inner dewar which contains- l i q u i d helium.  The dewars are made of pyrex glass and  s i l v e r e d by Brashear's chemical method (S2) such that two narrow s t r i p s  To follow page 20  PIRANI GAUGE  4  TO JACKETO F SIPHON  4  0 1 Trap  DIFFUSION PUMP  4  4  TO JACKET OF HELIUM DEWAR  BACKING ;PUMP M j : Mercury Manometer Mo : O i l Manometer  Fig.  6. A Schematic Diagram of the Vacuum S y s t e m .  To follow page 20  To Kinney Pump Transfer Siphon inlet Mica Window {fcs-«» To Waveguide System To Manometer" Brass Cap Rubber Sleeve  I  To Backing pump'  I  Helium Gas Return  Inner Dewar  German  Silver Guide  Outer Dewar  2^  Toluene Soaked Cotton  Resonator  F i g . 7 The Cryostat ( Cap Diam. 2.56" )  -21-  are l e f t for l i q u i d l e v e l observation.  The helium dewar encloses the  german-silver waveguide terminated by a Q-band resonator.  It i s topped  with a brass cap (2.56" O.D.) that carries also outlets for the helium transfer syphon, the manometers, the helium gas return l i n e and the Kinney pump for pumping over the l i q u i d helium to obtain temperatures below 4 . 2 ° K.  The b i g control valve V]_ i s bypassed by two progressively  smaller valves  and Vg to allow fine control of the pumping speed.  The lowest temperature normally obtained i n t h i s laboratory i s about 1 . 5 ° K.  A rubber sleeve over the cap and the dewar completes the vacuum  t i g h t compartment.  The whole assembly of cap and vacuum system i s  mounted•rigidly on a Dexion stand. As a r e s u l t of the small magnet gap available for experiments, has been necessary to make an open-bottomed outer dewar.  it  Cooling of the  lower parts of the helium dewar i s then achieved by a continuous stream of l i q u i d nitrogen flowing over i t s surface.  This method of cooling was  l a t e r found to be i n s u f f i c i e n t and wasteful.  A normal helium run lasted  only 2 to 3 hours.  In the experiment to be described i n chapter 4, the  Kinney pump i s not employed as i t i s uneconomical to lower the temperature below 4 . 2 ° K.  V  -22-  CHAPTER IV  EXPERIMENTAL PROCEDURE  An outline of a t y p i c a l paramagnetic resonance experiment at 4 . 2 ° K w i l l be given.  The procedure for room temperature performance i s  the  same except for the low temperature technique which i s then of no concern. A known amount of the sample under investigation i s mounted on the bottom of the cavity with n a i l varnish (colourless type).  Care must be  taken to use an amount that w i l l not overload the cavity.  The cavity  resonator i s then properly tightened to the german-silver guide and the klystron power supply switched on together with the fan which cools the klystron valve.  Saw-tooth modulation i s applied on the r e f l e c t o r so  that a whole mode can be swept through and displayed on a Tektronix scope 545A whose sweep i s synchronized with the modulating frequency. With the reflected power from the cavity displayed on the scope, the klystron i s mechanically tuned u n t i l a pip appears on the mode. To d i s t r i n g u i s h a true cavity resonance peak from peaks caused by reflections,  the following tests have been found useful and convenient.  By squeezing the german-silver waveguide, the guide wavelength increased without causing changes i n the frequency of the magnetic r a d i a t i o n .  is  electro-  Consequently, peaks caused by r e f l e c t i o n which i s  -23-  a function of the guide wavelength w i l l be shifted i n p o s i t i o n as seen on the screen while the resonant pip i s not affected.  As the german-  s i l v e r guide protrudes above the brass cap, t h i s method i s applicable at helium temperatures when other means of cross-checking i s d i f f i c u l t to achieve. e.g.  The other t e s t makes use of the effect of temperature,  cooling down the cavity with l i q u i d nitrogen.  As the cavity  shrinks i t s resonant frequency increases causing the pip to move across the screen without affecting the peaks from other r e f l e c t i o n . Once the resonance has been found, the tuning screws i n front of the coupling hole are adjusted to give a desired coupling condition. In a l l the experiments performed, the cavity i s s l i g h t l y undercoupled  •  (YD-  Now the double dewar cryostat i s ready for mounting.  After having  evacuated the inner dewar-, clean helium gas from a cylinder i s i n t r o duced into the dewar at a few centimeters above atmospheric pressure. The over-pressure i s maintained throughout the precooling to ensure that the helium gas i s not d i r t i e d when i t returns to the helium l i q u e f i e r i n the event of a s l i g h t leakage i n the vacuum system. before (3.5)  As mentioned  the outer dewar i s different from the conventional one.  In order to decrease the flow r a t e , cotton soaked with toluene i s used to block part of the flow (see F i g . 7).  However t h i s i s not very  satis-  factory because the adjustment i s almost impossible once the toluene has solidified.  Subsequently, the open end i s completely blocked off and.  l i q u i d nitrogen i s allowed to flow down only through three small tubings which can be seen i n Plate (II). necessary.  They may also be p a r t i a l l y blocked i f  -24-  When the helium gas inside the inner dewar has cooled down to the lowest temperature attainable, the l i q u i d helium transfer can s t a r t . The t r a n s f e r r i n g i s achieved by applying an over pressure of 4 cm mercury to the helium i n the can.  The return l i n e must be opened during  the transfer and after to allow the evaporated helium gas to return to the gas holder and the jacket of the transfer syphon i s evacuated to 50yU before the t r a n s f e r .  As soon as enough l i q u i d helium has been  syphoned over, the pressure on both sides of the syphon i s equalized. The helium can i s then removed and the syphon blocked.  Since the  dielec-  t r i c helium w i l l get into the c a v i t y , i t i s necessary to retune the cavity- as the resonant frequency w i l l be lowered by about 2.4%. At t h i s stage the magnet i s slowly r o l l e d i n place and the experiment i s ready to begin.  I t should be mentioned that for maximum  s t a b i l i t y of operation, the magnet current i s l e f t at about 6 amperes for about 2. hours previous to the experiment to allow the magnet and the power supply to reach thermal equilibrium.  The high i n t e n s i t y magnetic  f i e l d i s applied at r i g h t angle to the microwave magnetic f i e l d . To observe paramagnetic resonance, the k l y s t r o n modulation i s slowly turned down and the r e f l e c t o r voltage adjusted so that the klystron o s c i l l a t e s at the resonant frequency of the cavity at zero modulation.  Then a large f i e l d modulation i s superimposed on the main  f i e l d and the signal displayed on the screen.  The power input to the  cavity may be increased to allow v i s u a l observation without additional amplification.  The stub tuner i n arm 2 of the magic Tee ( F i g . 3)  is  carefully adjusted by varying i t s penetration and p o s i t i o n along the guide u n t i l a pure absorption mode appears.  The depth of penetration  -25-  of the tuner has been i n t e n t i o n a l l y increased to cause some microwave bucking.  However, no attempt has been made to find the optimum amount  necessary for high s e n s i t i v i t y performance.  F i n a l l y the signal  is  recorded with a small f i e l d modulation by synchronising the rotation of the motor of the recorder with the magnet current control d i a l . The detection scheme i s shown i n F i g . 5.:  MATCHED LOAD  STUB TUNER  KLYSTRON  MAGIC T  MODULATION COIL CAVITY  E.  STUB  IN 53  a.f.  TUNER  XTAL  AMP  ©  FILTER AMP  a..f. LOCK-IN  L-Y X  PHASE SHIFTER  Fig.  5 Block Diagram of a Single Modulation Spectrometer.  MOD  PEN RE COHOSH  -26-  CHAPTER V  EXPERIMENTAL RESULTS  5.1  Introduction Electron Spin Resonance (ESR) can be observed with any substance that has a structure with an unpaired electron (Chapter I ) .  Such sub-  stances are paramagnetic and they include atoms, free r a d i c a l s , b i r a d i c a l s , crystals containing paramagnetic ions, crystals with l a t t i c e defects and several other species.  However, the phenomenon  of microwave absorption i n paramagnetic s a l t s was only f i r s t  discovered  i n 1945 by Zavoisky (Zl) , while the paramagnetic resonance of free r a d i c a l s was f i r s t reported by Holden and others i n 1950 (H2, T2).  The  experimental technique was greatly advanced by Penrose (P2) i n 1949 when he discovered the method of magnetic d i l u t i o n i n order to resolve the hyperfine structures so often masked by spin-spin i n t e r a c t i o n . In t h i s chapter, copper sulphate pentahydrate and DPPH (diphenyl p i c r y l hydrazyl) are used to test the operation of the  spectrometer.  These two substances have often been employed as standards i n many ESR experiments for various reasons.  DPPH i s a stable free r a d i c a l that  gives a very strong signal of narrow l i n e width.  The copper s a l t has  been f u l l y studied and analysed both t h e o r e t i c a l l y and experimentally.  -27-  5.2  General Information  COPPER SULPHATE PENTAHYDRATE CuS0 '5H 0 4  2  The c r y s t a l i s tri-clihiC', of Space Group C^ and contains two molecules per unit c e l l  (B2).  Unit C e l l Dimensions a b c  Q  o Q  = 6.12 1  oC = 8 2 ° 16'  = 10.7  6  = 5.97  Y  r  = 1 0 7 ° 26' = 102  °  '  40  The a x i a l r a t i o i s a : b : c = 0.5715 = 1 = 0.5575.  Measurements  made by Krishnan and Mookherji (K3, K4) showed that i t i s magnetically anisotropic.  As pointed out by them, the asymmetry of the c r y s t a l l i n e  f i e l d acting on the paramagnetic ion i s the ultimate cause.  The most  complete paramagnetic resonance work was due to Bagguley and G r i f f i t h s (Bl) who found that the l i n e width varies greatly for different orientations of the c r y s t a l and at different wavelengths used. "  At  0.85 cm, the l i n e width at room temperature may vary from 25 to 450 gauss.  According to our measurement, the l i n e width also seems to  increase at low temperature.  l,l-DIPHENYL-2-PICRYL  HYDRAZYL (DPPH)  The stable c r y s t a l l i n e DPPH was the f i r s t free r a d i c a l studied by ESR (H2, T2).  Its s t r u c t u r a l formula i s  -28-  Subsequently, more d e t a i l studies have been done by Hutchison et a l (H3) and Kikuchi et a l ( K l ) . election associated with i t ,  Since each molecule has one unpaired a very intense signal i s obtained.  The  g-value i s s l i g h t l y anisotropic being i n the range of 2.0035 to ,2.0041 depending on o r i e n t a t i o n .  For a p o l y c r y s t a l l i n e sample, a  half-width of 3.7 Oe i s observed at 3 cm wavelength (H3).  However,  the-half-width i s only 1.8 gauss when the external f i e l d i s 3 gauss. Although no special attention has been paid to the measurement of l i n e width, our value i s about 5 gauss i n d i c a t i n g a p o s s i b i l i t y of further broadening under higher f i e l d  5.3  Results  intensity.  1  The signals obtained from 2.0 mg of CuSO^'S^O c r y s t a l are shown i n F i g . 8.  The c r y s t a l was mounted on i t s a* face with the b-axis  approximately at r i g h t angle to the s t a t i c magnetic f i e l d .  The  experiment was carried out at room temperature as well as at 4 . 2 ° K  To follow page 28  (a)  At  300°K  (b) At 4 . 2 ° K  F i g . 8 Signals F r o m 2mg of C u S 0  Fig. 9  4  . 5 H O Single C r y s t a l  Signal F r o m 0 . 2 m g of Powder DPPH  -29-  and the modulating f i e l d used i n each case i s about one-fifth of the l i n e width value. Figure 9 shows the signal from 0.2 mg of DPPH i n p o l y c r y s t a l l i n e form.  In t h i s case the modulating f i e l d i s about 0.7 gauss as  measured by the voltage induced i n a c o i l located at the centre of the magnet gap. The s e n s i t i v i t y Table 1. P  Q  deduced from these measurements i s shown i n  The relevant data for c a l c u l a t i o n being power input  1 mW, bandwidth  A v> = 1 cps, unloaded cavity Q = 3000, Q  noise figure F = 1, f i l l i n g factor 400, and 4 gauss.  ^  = 1, l i n e width  Theoretical s e n s i t i v i t i e s have been calculated  using the equation (2.8)  (Fl).  Mass sensitivity  where  F  A H = 150,  (2.8)  t o t a l noise factor of the detector system electronic magnetic moment molecular weight of the sample Avogadro's number  k  Boltzmann's constant  T  temperature i n  K.  -30-  TABLE 1  SENSITIVITY. OF Q-BAND SPECTROMETER OBTAINED  Sample CuS0 '5H 0 4  2  DPPH  Temperature  Ultimate S e n s i t i v i t y  Experimental S e n s i t i v i t y  300° K  7 • lo--10 gm  2 •10"-4 gm  4.2° K  -13 3 •10" gm  4 •10--6 gm  300° K  2 10"-11 gm  4 •10"-6 gm  It seems that the experimental s e n s i t i v i t y  i s far from s a t i s f y i n g .  However, i t must be mentioned that the actual f i l l i n g factor was calculated to be 0.004, 250 times less than the i d e a l one.  A l s o , the  noise figure that can be normally achieved i s not 1, but of the order 10.  Therefore, the present s e n s i t i v i t y  could be e a s i l y improved by a  hundred f o l d by increasing the f i l l i n g factor alone.  Further improve-  ment could be achieved by reducing the noise l e v e l of the system which i s reckoned to be a b i t high although the true value was not determined. For comparison, we give the s e n s i t i v i t y  of various  that have been s p e c i a l l y designed for high s e n s i t i v i t y  spectrometers operation.  These are shown i n Table 2 for the testing sample DPPH only.  -31-  TABLE 2  COMPARISON OF SENSITIVITY OF DIFFERENT SPECTROMETERS AT 290° K  •Type .  Operating Band  Sensitivity  Single f i e l d modulation  X band  3x10  _  Super heterodyne detection  X  8xl0  Reference  g  gm  PI  gm  HI  K "  9 8x10 ' gm  B6  modulation  K "  lxlO  B7  Single f i e l d modulation  Q "  ~ 10  Single f i e l d modulation  "  '  9  _:7  Double f i e l d  _  - 1 1  gm  gm  -32-  CHAPTER VI  CONCLUSION AND DISCUSSION  An 8 mm s o l i d state spectrometer has been tested and found satisfactory i n most respects.  Although the s e n s i t i v i t y s t i l l  falls  short of the t h e o r e t i c a l l y predicted value, i t i s comparable to the most sensitive spectrometers reported.  The discrepancy probably l i e s  i n the fact that the external interferences have not been t o t a l l y eliminated. i n nature.  The external interferences may be e l e c t r i c a l or mechanical They cause i n s t a b i l i t i e s of about five to ten times the  l e v e l of random noise  (HI).  Frequency i n s t a b i l i t y i s not a l i m i t i n g  factor as the Q of the cavity i s only a few thousand. interference has been eliminated.  Electrical  Mechanical interference coming from  building vibrations has not been taken care of although rather s t r a i g h t forward shock mounting should eliminate them. The s e n s i t i v i t y can be increased by improved methods of detection. Using.double f i e l d modulation, an  improvement of about 1000 should be  possible as has been demonstrated by Buckmaster (B7).  However i t may  not be an easy task to overcome the problems involved i n high'frequency modulation since we are now working at a shorter wavelength.. The method of superheterodyne detection applied to the present setup should t h e o r e t i c a l l y give 10^ times better s e n s i t i v i t y than a  -33-  c r y s t a l or bolometer detector (Ml).  This i s mainly because of the  greatly reduced c r y s t a l noise which i s inversely proportional to frequency ( T l ) .  Under p r a c t i c a l conditions, only 5-10 times improve-  ment has been achieved ( F l ) .  Moreover, the need for an a u x i l i a r y  o s c i l l a t o r and an automatic frequency control system to keep the frequency difference between the two o s c i l l a t o r s constant makes the superheterodyne more complicated.  The a u x i l i a r y o s c i l l a t o r may i n  i t s e l f be a further source of noise. High frequency modulation i s not very satisfactory because the increased modulation frequency introduces more pickup o r i g i n a t i n g from the magnetic forces of the s t a t i c f i e l d i n t e r a c t i n g with the eddy currents induced i n the cavity walls by the a.c.  f i e l d component.  With s u f f i c i e n t effort,such as the use of nonconducting walls with plated i n t e r i o r surfaces, i t may be possible to reduce the eddy currents ( L I ) . The best approach, i f ultimate s e n s i t i v i t y i s not absolutely necessary,  seems to be the use of bolometer.  The only change needed  then i s to decrease the modulation frequency since bolometer functions better below 100 cps.  Also the problem incurred i n designing new  detecting instruments w i l l be r e l a t i v e l y simple and quickly achieved.  -34-  APPENDIX  The c i r c u i t diagrams used are collected together i n t h i s Appendix. Unless otherwise stated the values for the r e s i s t o r s are i n ohms and the capacitors i n microfarads. Page 35  C i r c u i t 1.  Magnet Current Supply  C i r c u i t 2.  Modulation Supply  36  C i r c u i t 3.  High Gain Audio Amplifier  37  C i r c u i t 4.  Phase Shifter  38  C i r c u i t 5.  F i l t e r Amplifier  38  C i r c u i t 6.  Phase Sensitive Detector  39  All Resistors "Ohmite" Circuit 1. Magnet Current Supply ( 3 chassis in series ).  A  f3 6AS7G  Oscillator at 140cps s  I0K>*  6AS7G  14*~'fuEes" in" parallel 680  680  HE  68) IM  220K> 3.4>  J .05ZZ >  Hammond 263C60  I20V.A.C  < .02 470K  J-500 I TMFD  T20  1  46  20H I50mA 220VDC + ^ ^ l l  6 ^ 3 V . A . C . 6AU6 ^)  6A87G  I5(150W)  Pilot  Circuit 2.  Modulation Supply.  MOD Coil 5 ohms D.C.  u  T  5693  5693  5693  To filter amplifier  Circuit 3. High Gain Audio Amplifier.  -38-  +  250V +  Circuit 4 . Phase Shifter.  Values for Twin-Filter are 1% A l l Others 10% and |W  Circuits.  Filter-Amplifier.  12AU7  ' + 250V  ,Balance  -VSA*  20KWW 12AT7  uuuu  1  r^-V  Hammond T20D  80  M  + 2 50V 4.7M^  ,7  __  6AU6 4 OK  Recorder  4  <*±  T  Circuit 6.  -05  .11  JL J .  T  .22  1  T  T  ± 1 1  T T  Phase Sensitive Detector.  .5  -40-  BIBLIOGRAPHY  Bl  Bagguley, D.M.S. and G r i f f i t h s , J . H . E . , Proc. Roy. Soc. A201 (1950) 366.  B2  Beevers,  C A . and Lipson, H. , Proc. Roy. Soc. A146 (1934) 570.  B3  Bethe, H . A . , Ann. Phys., Lpz. 3 (1929) 133.  B4  Bleaney, B. and Stevens, K.W.H., Rept. Prog. Phys. 16 (1953) 108.  B5  Bowers, K.D. and Owen, J . , Rept. Prog. Phys. 18 (1955) 304.  B6  Buckmaster, H . A . , Ph.D. Thesis, University of B r i t i s h Columbia (1955).  B7  Buckmaster, H.A. and S c o v i l , H . E . D . ,  Fl  Feher, G . , B e l l Syst. Tech. J . 36 (1957) 449.  Gl  Garwin, R . L . , Rev. S c i . Instr. 29 (1958) 223.  G2  Ginzton, E . L . , "Microwave Measurements" (McGraw-Hill, New York,  Can. J . Phys. 34 (1956) 711.  Toronto and London, 1957). HI  Hirshow, J . M . and Fraenkel, G . K . , Rev. S c i . I n s t r .  26 (1955) 34.  H2  Holden, A . , K i t t e l , C . , M e r r i t t , F . R . and Yager, W.A., Phys. Rev. 77 (1950) 147L.  H3  Hutchison, C A . J r . , Pastor, R . C and Kowalsky, A . G . , J . Chem. Phys. 20 (1952) 534L.  II  Ingram, D . J . E .  "Spectroscopy at Radio and Microwave Frequencies"  (Butterworths,  London, 1955).  Kl  Kikuchi, C. and Cohen, V.W., Phys. Rev. 93 (1954) 394.  K2  Kramers, H . A . , Proc. Acad. S c i . Amst. 33 (1930) 959.  K3  Krishnan, K . S . and Mookherji, A . , Phys. Rev. 50 (1936) 860.  K4  Krishnan, K . S . and Mookherji, A . , Phys. Rev. 54 (1938) 533.  Ll  Lambe, J . , Ager, R . , Rev. S c i . I n s t r . 30 (1959) 599N.  L2  Low, W., "Paramagnetic  Resonance i n Solids" Supp. 2, Solid State  Physics Series (Academic Press, New York and London, 1960). Ml  Misra, H . , Rev. S c i . I n s t r . 29 (1958) 590.  01  Orbach, R. , Proc. Roy. Soc. 264A (1961) 458.  PI  Pake, G.E. , Weissman, S . I . and Townsend, J . , Disc. Faraday Soc. 19 (1955) 147.  P2  Penrose, R . P . , Nature Lond. 163 (1949) 992.  P3  Pryce, M . H . L . , Proc. Phys. Soc. A63 (1950) 25.  P4  Pryce, M . H . L . , and Stevens, K.W.H., Proc. Phys. Soc. A63 (1950) 36.  51  Schuster, N . A . , Rev. S c i . Instr. 22 (1951) 254.  52  Strong, J . , Neher, H.V. , Whitford, A . E . , Cartwright, C H . and Hayward, R . , "Procedures i n Experimental Physics" 22nd p r i n t i n g (Prentice H a l l , New Jersey, 1961).  Tl'  Torrey, H.C. and Whitmer, C . A . , "Crystal Rectifiers"  (McGraw-Hill,  MIT Radiation Lab. Series, V o l . 15, p. 187, 1948). T2  Townes, C H . and Turkevich, J . , Phys. Rev. 77 (1950) 148.  VI  V a l l e y , G . E . and Wallman, H . , "Vacuum Tube Amplifiers", MIT'Radiation Lab. Series, V o l . 18 (McGraw-Hill, New York, Toronto and London, 1948).  V2  Van Vleck, Phys. Rev. 74 (1948) 1168.  Wl  White, G . K . , "Experimental Techniques i n Low-Temperature  Physics",  (Clarendon Press, Oxford, 1959). W2  Wilson, I . C , Schramm, C'.W. and Kinzer, J . P . , B e l l Syst. Tech. J . 25 (1946) 408.  -42-  Yl  Y a r i v , A. and Clapp, F . , Rev. S c i . I n s t r .  Zl  Zavoisky, E . , J . Phys. USSR 9 (211)  1945.  30 (1959) 684.  T o follow page  PLATE III  GENERAL VIEW OF THE APPARATUS  

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